Back in the day with dimensional lumber joists, it was common to box out an area for something like a tub drain that could not be moved due to floor plan layout. I remember seeing 2×8 or 2×10's doubled up on each side that a joist-box was needed. Then normally the floor joist designated for running where the drain box was made would stop short and hang on a perpendicular short joist spanning to both sides of the doubled joists.
However, what is the most economical way to do that with today's modern I-Joists? It would be rather expensive to run double I-Joists on each side, and it would seem hard to fit something like an LVL block in place between two joists because there is not an engineered LVL hanger I can find and I don't think the two side I-Joists would be rated to carry that end load especially if it's something like a tub full of water on this span.
Best Answer
Since I-Joists are an engineered system, it's vitally important to follow the specific instructions (including the "you can't do that" instructions) of your specific manufacturer for the specific product you have, as they are not all the same. Mine came with at least 4-5 double-sided pages of detailed instructions covering common issues.
I would strongly question the wisdom of following a floor plan layout destined for I-joists which parked a tub drain going through where an I-joist should be. That's poor planning for the construction method. If you are in the "as yet unbuilt" stage (which it sounds like) then redesigning the joist placement or tub placement so that they do not conflict would be the best approach. Generically, a single extra joist and different joist spacing (such as 19.2 inches rather than 24, or 12 rather than 16) in the immediate area should be an adequate solution that does not involve the compromises of mid-span support. Alternatively, a tub with a drain in a different location might solve it, without moving the tub itself.